Topic 11 – Electromagnetic induction
Formative Assessment
PROBLEM SET
NAME: ________________________________ TEAM:__
THIS IS A PRACTICE ASSESSMENT. Show formulas, substitutions, answers, and units!
Topic 11.1 – Electromagnetic induction
An electron is in a straight wire conductor that is being pulled perpendicular to a magnetic field having a
strength of B = 0.150 T at a speed of 45.0 ms-1. The wire is oriented in an east-west direction and is being
pulled to the south. The B-field is oriented downward.
1. What is the magnitude of the magnetic force that the electron experiences during the motion of the
wire through the magnetic field?
2. What is the direction of the force? Explain how you find this out.
The following questions are about moving conductors and moving magnetic fields.
3. Describe the inducing of an emf by relative motion between a conductor and a magnetic field. Give
two scenarios which exemplify this relative motion.
4. Derive the formula  = BVℓ for the emf induced in a straight conductor of length ℓ traveling
perpendicular to a magnetic field having a magnitude B at a velocity v.
A wire having a length of 20.0 m is propelled through the air in a direction perpendicular to its length at
150. m/s in a magnetic field that is perpendicular to the plane of its velocity, and having a strength of
0.015 T.
5. What is the induced emf in the wire?
6. If a resistor of 12.0  is connected to the ends of the wire, what will its current be?
7. What would be the power dissipated in the resistor?
The following questions are about magnetic flux and magnetic flux linkage.
8. Define magnetic flux and magnetic flux linkage.
9. Define magnetic flux density. What is another word for this quantity?
10. Name three ways to make the magnetic flux change.
11. Describe how the coil of a generator rotating in a magnetic field produces an induced emf.
The following questions are about Faraday’s law and Lenz’s law.
12. State Faraday’s law.
13. State Lenz’s law.
14. Formulate a convincing argument for Lenz’s law. In other words, why must the induced flux change
act in such a way as to minimize the original flux change?
A wire is wrapped around a toilet paper tube (diameter 5.0 cm) and
connected to a voltmeter, as shown. A bar magnet (B = 0.50 T) is
oscillating in and out of the tube 75 times each minute, as shown by the
double arrow. When thrust in right-ward direction, the voltmeter needle
deflects to the right to a maximum of 14 V.
15. Describe the motion of the needle over time.
16. If you increased the oscillation rate to 125 times each minute, what
would the maximum voltage read?
17. How many more loops would you need to add if you wanted the maximum voltage to read 20. V?
Assume the oscillation rate is back to its original value.
A coil of wire resting on a tabletop and having 100 turns and an area of 3.14 cm2 is immersed in a
magnetic field (0.90 T) which is pointing upward.
18. What is the angle that the magnetic field makes with the direction of the area?
19. What is the flux through a single loop?
20. What is the flux linkage through the coil?
21. What is the induced emf if the magnetic field remains constant?
22. If the magnetic field decreases to 0.45 T in 0.25 s, what is the rate of change of the flux linkage
through the coil?
23. What, then, is the induced emf?
24. What is the direction of the induced current in the coil, as viewed from above the table? Which law
tells you this?
A coil having 250 turns is subjected to a time-dependent magnetic flux as shown
in the graph.
25. What is the flux at t = 0.0015 s?
26. What is the flux linkage at t = 0.0015 s?
27. What is the magnitude of the emf induced in the coil?
A coil having an area of 2.510-3 m2 and 150 turns is
moved in the magnetic field of a magnet between P and
Q as shown. The distance the coil is from the face of the
magnet is x. The variation in strength of the magnetic
field with x is shown in the graph.
28. What is the flux linkage when the coil is located at x
= 1.25 cm?
29. What is the flux linkage when the coil is located at x
= 2.75 cm?
30. If the coil was moved from the first position to the second one in
125 ms, what is the induced emf in the coil?
This question is about electromagnetic induction. A small coil is placed with its plane
parallel to a long, current-carrying wire as shown.
31. State Faraday’s law of electromagnetic induction.
32. Use the law to explain why, when the current in the wire changes, an emf is
induced in the coil.
33. Such a coil may be used to measure large alternating currents in a high voltage cable. Identify one
advantage and one disadvantage of this method.
Topic 11.2 – Power generation and transmission
A rectangular coil of wire having dimensions 2.5 cm by 3.2 cm has 250 turns. It is rotating at a frequency
of 60 Hz in a magnetic field having a strength of 1.5 T.
34. What is its peak voltage 0?
35. What is the time dependence of its emf?
36. If the frequency is increased to 80 Hz, what is this generator’s peak voltage?
37. If the original frequency is tripled, what is the generator’s peak voltage?
The following questions are about root mean square (rms) values.
38. Discuss what is meant by the root mean square (rms) value of an alternating current or voltage. Why
is it used, instead of the straight-forward mean?
39. What is the significance of rms values in the context of power usage?
40. State the relation between peak and rms values for sinusoidal currents and voltages.
42. Find the peak voltage.
em f / V
The graphs of voltage and current for an ac circuit containing a resistor are shown.
41. Find the rms voltage corresponding to the
40
induced emf whose graph is shown.
43. Find the angular frequency of the coil that is
producing this emf.
20
0
20
40
30
10
t / ms
-20
-40
2
1
I/A
44. Find the maximum flux linkage of the coil that is
producing this emf.
0
-1
45. Find the rms current from the graph.
46. Find the peak current.
-2
20
10
40
30
t / ms
47. Write the equation which shows the time variation of the current.
48. Find the resistance of the circuit.
49. What is the average power dissipated by the circuit?
The following questions are about ideal transformers.
50. Describe the operation of ideal transformers.
51. Show that for an ideal transformer Is / Ip = Vp / Vs.
A transformer having 250 turns in its primary winding has a 60 Hz input
voltage of Vin = 120 VAC. It is desired that Vout should be 16 VAC.
52. How many turns should the secondary winding have?
Vin
Primary
Vout
Secondary
53. If the current in the primary winding is 1.25 A, what will the current in
the secondary winding be?
54. What is the frequency of the output voltage?
55. If the frequency doubles, describe how this will affect power losses due to magnetic hysteresis and
eddy current heating.
The following questions are about power transmission and the power grid.
56. Outline the reasons for power losses in transmission lines.
57. Outline the reasons for power losses in real transformers. Which is more significant?
58. Explain the use of high-voltage step-up and step-down transformers in the transmission of electrical
power.
59. A power plant produces a 60 Hz alternating voltage having Vrms = 400 V. A step-up transformer is
needed to raise the plant’s voltage to 765 kV. Find the ratio of Ns / Np needed in the transformer.
60. A step down transformer is needed to reduce a 765 kV transmission voltage to 13 kV at a factory.
Find the ratio of Ns / Np needed in the transformer.
A power transmission cable having a diameter of 8.0 cm is made of aluminum which has a resistivity of
5.210 -8 m.
61. Find the cross-sectional area of the cable in m2.
62. Find the resistance of this cable if it provides electricity to a township 125 km away from a power
plant.
63. Suppose this cable is used to supply a township with 220 MW of energy at a transmission voltage of
765 kV. What is its current? What is its heat loss. What percentage of the overall energy
transmission is this?
A circuit that consists of four diodes and a resistor is shown.
64. What is this circuit called? What does it do?
65. Label the top AC power supply terminal with a (+), and with a red
pencil trace the positive current through the circuit all the way to the
load resistor and the correct DC output terminal.
66. Label the bottom AC power supply terminal with a (–), and with a green pencil trace the negative
current through the circuit all the way to the load resistor and the correct DC output terminal.
67. If the AC power supply now reverses its polarity, determine which output terminal is (+) and which is
(–).
68. If the input voltage is a sine wave, sketch the input and output voltage for one cycle.
69. What electrical component could you add to the circuit to keep the voltage more stable?
Topic 11.3 – Capacitance
The following two questions are about the definition of capacitance.
70. What is the definition of capacitance and what is its unit of measure?
71. A 1.50-V cell is used to fully charge a 425 F capacitor. How much charge was transferred from the
negative to the positive plate?
Three 425 F capacitors are connected in parallel to a 6.00 V battery.
72. What is the equivalent capacitance?
73. What is the charge on each capacitor?
74. What is the voltage on each capacitor?
Three 425 F capacitors are connected in series to a 6.00 V battery.
75. What is the equivalent capacitance?
76. What is the charge on each capacitor?
77. What is the voltage on each capacitor?
Three 425 F capacitors are connected in the combination shown to a
6.00 V battery.
78. What is the equivalent capacitance?
79. What is the charge on each capacitor?
80. What is the voltage on each capacitor?
The following questions are about parallel plate capacitors.
81. Describe three ways you can increase the capacity of a parallel plate capacitor.
82. Explain the function of the dielectric in a parallel plate capacitor. How does it increase the capacity?
A 425 F capacitor will be manufactured using a dielectric having a permittivity of 5.250 and circular
plates having a diameter of 1.75 cm.
83. What should the plate separation (and the thickness of the dielectric) be?
84. Is it likely that this large a capacity could be constructed using parallel plate architecture? ___ Why?
85. What type of capacitor would be capable of providing this capacity?
The following questions are about the electrical energy stored in a capacitor.
86. Provide a proof that the energy stored in a capacitor is given by E = (1/2)qV. Hint: Use W = area
under the V vs. q graph, and that C = q / V.
87. Provide a proof that the energy stored in a capacitor is given by E = (1/2)CV2.
88. Find the energy stored in a 425 F capacitor charged up to 6.00 V.
89. Provide a proof that the energy stored in a capacitor is given by E = q2/ (2C).
C1 is initially charged to 6.00 V. C2 is initially uncharged.
90. What is the charge on C1’s plates?
91. The switch is closed, connecting C1 to C2. What are the charges on the
plates of C1 and C2?
A capacitor having no dielectric has a capacitance of 150. pF. It
is charged up to 6.00 V by momentarily attaching it to a
battery, and then disconnecting it.
92. What is the energy stored in the capacitor at this voltage?
93. What is the charge on the capacitor?
94. A dielectric having a dielectric constant of 4.25 (this means
a permittivity of 4.250) is now carefully inserted between
the plates of the capacitor. What is its new capacitance?
95. What is the charge on the new capacitor? What is the voltage on the new capacitor?
96. What is the energy stored in the new capacitor? Explain the discrepancy between this answer and
that of the same capacitor without the dielectric.
The following questions are about a charging RC circuit. The capacitor is
initially uncharged.
97. Make a sketch graph showing the family of curves representing the
voltage across the resistor after the switch is closed and as RC
increases. Show at least three different RC curves, and label them
“low,” medium,” and “high.”
98. Make a sketch graph showing the family of curves representing the
voltage across the capacitor after the switch is closed and as RC
increases. Show at least three different RC curves, and label them “low,” medium,” and “high.”
A circuit constructed of a resistor R and a capacitor C has a switch
which can be made to charge and discharge the capacitor.
99. Label the switch position which charges the capacitor with an
“A” at the small circle in the schematic.
100. Label the switch position which discharges the capacitor with
a “B” at the small circle in the schematic.
101. Draw arrows in the discharge loop showing the direction of
current flow during discharge.
102. What equation does Kirchhoff’s rule for V produce during
discharge? Your final equation should have only these variables: q, q, t, R and C.
103. Show that the time constant  = RC has the reduced unit seconds.
A 425 F capacitor is charged to 6.00 V. It is then discharged through a 20.0 M resistor.
104. Find the time constant.
105. Find the initial charge on the plates.
106. Find the charge on the plates exactly one time constant after discharge has begun.
107. What percent of the original charge is this?
108. Find the capacitor’s voltage 4250 s after discharge begins.
109. Find the instantaneous current at t = 4250 s.
110. Find the half-life of the capacitor’s voltage.
A timer using a capacitor and a resistor needs the RC circuit to have a half-life of 275 seconds. It will be
using a capacitor of 125 F, initially charged to a voltage of 6.00 V.
111. What should the value of the time constant be?
112. What value should the resistor have?
113. What will the capacitor voltage be at t = 275 s?